32 Kinematics of a 5Axis Milling Machine

The benefits of 5-axis machining arise from the ability of the machine to position the cutting tool in an arbitrary orientation with respect to a workpiece. This ability is exploited by the authors of numerous papers. The reader is typically shown an illustration of a tool floating in space above a workpiece. The mechanics of actually placing a tool in the desired location is in many cases not discussed. This phenomenon is largely due to the nature of 5-axis machining and to the nature of research. 5-axis machining is highly dependent on the configuration of the target machine. Almost every 5-axis CNC machine requires a different post-processor to account for the effect of the machines rotational axes. In fact, the post-processor requires information about the workpiece setup and tooling before it can convert generic cutter location data into specific machine-dependent G-code. Even after post-processing, the same tool path executed on different CNC machines will produce noticeably different results. For these reasons, this section on machine kinematics has been included in this chapter.

5-axis milling machines are classified by the combination and order of their linear (T) and rotational (R) axes. For example, a machine with three translations and two rotations would be specified as a TTTRR machine. There are many possible combinations of these axes that can be used to produce a 5-axis milling machine. However, as Kiridena [26] points out, there are in fact only three commonly used machine configurations:

1. RRTTT: a tilt-rotary table mounted on three linear axes usually referred as a the tilt-rotary type 5-axis machine

2. TTTRR: three linear axes with the cutter oriented by two rotary axes, commonly called a wrist type or Euler type 5-axis machine

3. RTTTR: a rotary table mounted on three linear axes and a single rotary axis for the tool

These three types of 5-axis configurations are illustrated in Fig. 3.2. The other possible configurations such as TRTTR are generally not used because of the difficulty in designing a machine with a mixture of rotational and linear axes that meets the stiffness requirements for a milling machine. Each of the configurations shown has its own advantages and disadvantages. The wrist type machines are the simplest to program, can be built to accommodate very large workpieces, but tend to be less rigid than the other configurations. They are best suited to surface machining. Tilt-rotary table type machines excel at 5-sided machining and tend to be stiffer than other configurations. However, they are more prone to setup error and may not be able to accept large workpieces.

When programming a CNC machine, the motion of each joint must be specified in order to achieve the desired position and orientation of the tool relative to the workpiece. This is referred to as the inverse kinematics problem. The programmer will also need to know the resulting position and orientation of the tool for a given set of joint commands in order to verify that the tool path is correct.

tilt-rotary table type wrist type rotary table type

FIGURE 3.2 Typical 5-axis machine configurations.

FIGURE 3.2 Typical 5-axis machine configurations.

FIGURE 3.3 Kinematics of a tilt rotary table type 5-axis machine.

This is referred to as the forward or direct kinematics problem. The following sections describe the forward and inverse kinematics of the tilt-rotary table type 5-axis milling machine and the wrist type 5-axis milling machine.